What is the general solution for 3cos(x)=2sin(x) ?

The general solution for 3cos(x)=2sin(x) is x=0.98279…+pin

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3cos(x)=2sin(x)

3 cos (x) = 2 sin (x)

x = 0.98279 \dots + πn

Degrees

x = 56.30993 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 cos (x) = 2 sin (x)

Rewrite using trig identities

3 cos (x) = 2 sin (x)

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{3 cos ( x )}{cos ( x )} = \frac{2 sin ( x )}{cos ( x )}

Simplify

3 = \frac{2 sin ( x )}{cos ( x )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

3 = 2 tan (x)

Switch sides

2 tan (x) = 3

2 tan (x) = 3

Divide both sides by

2

2 tan (x) = 3

Divide both sides by

2

\frac{2 tan ( x )}{2} = \frac{3}{2}

Simplify

tan (x) = \frac{3}{2}

tan (x) = \frac{3}{2}

Apply trig inverse properties

tan (x) = \frac{3}{2}

General solutions for

tan (x) = \frac{3}{2}

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{3}{2}) + πn

x = arctan (\frac{3}{2}) + πn

Show solutions in decimal form

x = 0.98279 \dots + πn

2 cos^{2} (θ) - cos (θ) = 1, 0 \leq θ \leq 2 π

tan (x) - 3 = 0, 0 \leq x \leq 2 π

1 = tan (0 + c)

4 sin^{2} (x) = 3 - 4 sin (x)

tan (θ) = - \frac{2}{2}

What is the general solution for 3cos(x)=2sin(x) ?
The general solution for 3cos(x)=2sin(x) is x=0.98279…+pin